Details

sample1.6m (39.9%)

Algorithm
77×intervals
Results
34.4s43895×body1280valid
13.5s14355×body10240exit
11.5s30404×body640valid
6.9s201914×body80valid
4.7s27621×body320valid
4.6s152017×body80nan
3.0s35932×body160valid
2.6s150853×pre80true
771.0ms3076×body2560valid
381.0ms7914×body160nan
377.0ms4112×pre10240exit
95.0ms8228×pre80false
61.0ms220×body5120valid

prune1.1m (28.1%)

series40.1s (16.9%)

Calls

486 calls:

736.0ms
(cbrt (+ (fma (* 1.5 (pow (log 2.0) 2)) x (pow (log 2.0) 3)) (- (* (* 0.75 (pow x 2)) (+ (log 2.0) (pow (log 2.0) 2))) (* 3/2 (/ (* (pow (log 2.0) 2) (pow x 2)) (pow 2.0 2))))))
627.0ms
(- (* (* 0.75 (pow x 2)) (+ (log 2.0) (pow (log 2.0) 2))) (* 3/2 (/ (* (pow (log 2.0) 2) (pow x 2)) (pow 2.0 2))))
610.0ms
(/ (* (sin phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin (- lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
439.0ms
(* (hypot (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (- phi1 phi2)) R)
431.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)

simplify13.5s (5.7%)

Algorithm
220×egg-herbie

regimes10.8s (4.6%)

Accuracy

Total 38.3b remaining (30.5%)

Threshold costs 5.9b (4.7%)

6.0b42.4%Quotient of products
5.9b57.2%Cubic critical, narrow range
5.1b27.5%Cubic critical, medium range
5.0b82.9%Quadratic roots, full range
4.5b84.4%Cubic critical

rewrite8.7s (3.7%)

Algorithm
144×rewrite-expression-head
Calls

486 calls:

574.0ms
(- (* (/ (sqrt 1.0) (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ (sqrt 1.0) (cbrt (+ x 1.0)))) (/ (/ (/ 1.0 (cbrt (- x 1.0))) (cbrt (- x 1.0))) (cbrt (- x 1.0))))
344.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))
259.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
203.0ms
(* (* (* (- (/ (* m (- 1.0 m)) v) 1.0) (sqrt m)) (sqrt (sqrt m))) (sqrt (sqrt m)))
162.0ms
(* (/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3))) (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b)))))
Rules
14982×times-frac
12989×*-un-lft-identity
12746×add-sqr-sqrt
8727×add-cube-cbrt
5818×prod-diff
4237×cbrt-prod
1894×add-exp-log
1684×add-cbrt-cube
1593×difference-of-squares
1398×distribute-lft-out--
1339×unpow-prod-down
1257×sqrt-prod
1208×associate-*r*
1041×pow1
984×distribute-rgt-neg-in
970×associate--r+
808×distribute-lft-neg-in
733×add-log-exp
640×distribute-lft-out
623×cube-prod
611×div-inv
610×associate-/l*
557×associate-/r/
497×distribute-rgt-in distribute-lft-in
488×expm1-log1p-u
486×log1p-expm1-u
479×associate-/r*
466×div-exp
460×sqr-pow
458×prod-exp
422×associate-*l*
401×cbrt-undiv
399×cbrt-unprod
375×flip--
374×flip3--
309×fma-neg
307×fma-def
233×flip-+
232×flip3-+
209×neg-mul-1
208×associate-*r/
203×unswap-sqr
185×frac-times
181×cbrt-div
174×pow-prod-down
155×log-pow
152×exp-prod
141×unpow3 cube-mult
128×associate-*l/
125×log-prod
110×clear-num sub-neg frac-2neg
98×*-commutative
86×associate-/l/
76×sqrt-div
75×sqrt-pow1
69×diff-log
64×swap-sqr
61×pow-unpow
60×tan-quot
57×sum-log pow-exp
56×pow-to-exp
51×pow-prod-up
48×pow1/2
46×cos-sum unpow2
45×div-sub
44×pow1/3
43×+-commutative
36×rem-sqrt-square
35×pow-sqr
34×sin-sum neg-sub0
28×pow-plus log-div
27×frac-sub
24×pow-pow
23×fma-udef pow2 sin-mult
21×frac-add
20×associate-+l-
19×neg-log 1-exp
18×distribute-rgt-out cos-mult rem-log-exp sin-diff
17×cube-div
15×hypot-def rec-exp
14×rem-cube-cbrt cos-diff
11×acos-asin
10×rem-cbrt-cube
9×sin-cos-mult distribute-frac-neg associate--l- associate-+r+
8×associate-+l+
7×associate-+r- sum-cubes expm1-udef
6×exp-diff sub-div associate--l+ distribute-neg-frac
5×rem-exp-log acos-neg associate--r- distribute-rgt-neg-out
4×un-div-inv inv-pow distribute-lft-neg-out pow-flip exp-sum
3×expm1-log1p unpow-prod-up
2×sin-neg log1p-udef distribute-lft1-in exp-neg log1p-expm1 hypot-udef unsub-neg sqrt-unprod
1×sqrt-pow2 e-exp-1 rem-square-sqrt asin-acos distribute-rgt-out-- exp-to-pow

localize2.2s (0.9%)

bsearch494.0ms (0.2%)

end1.0ms (0.0%)